Anisotropy parameters for the effective description of crystalline color superconductors

In the high density low temperature limit, quantum chromodynamics (QCD) exhibits a transition to a phase characterized by color superconductivity and by energy gaps in the fermion spectra. Under specific circumstances the gap parameter has a crystalline pattern, breaking translational and rotational invariance. The corresponding phase is the the crystalline color superconductive phase [or Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase]. In the effective theory the fermions couple to the phonon arising from the breaking of rotation and translation invariance. We compute for the single-plane-wave condensate ansatz the parameters of the low energy effective Lagrangian describing the motion of the free phonon in the high density medium and derive the phonon dispersion law.